Rotary offset printing machines having printing stations in which paper is guided in an essentially vertical path from beneath the machine and then in an essentially horizontal path into the printing station, leaving space beneath the horizontal path for access to the printing systems located beneath this horizontal portion of the path (see, for example: "Techniken, Systeme, Maschinen", page 9, FIG. 17b, by Oscar Frei; published by Polygraph-Verlag) are known. Guiding the paper web in the aforementioned path provides for relatively good accessibility to the lower cylinders of the printing system. Difficulties arise, however, particularly when used for newspaper printing, to change plates of the cylinders loated above the horizontal portion of the paper web path, since access to those cylinders is impeded by the paper web itself. Of course, it is possible to relocate the paper path by placing the vertical portion close to the printing stations, so that free access to the upper cylinders can then be provided; yet, if that is done, access to the cylinders of the lower printing system, that is, the one beneath the remaining horizontal portion of the paper path, is then impeded, since the vertical portion close to the lower printing system will then be covered by the paper web.